Related papers: Conditional constrained and unconstrained quantiza…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
The Born rule for probabilities of measurement results is deduced from the set of five assumptions. The assumptions state that: (a) the state vector fully determines the probabilities of all measurement results; (b) between measurements,…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
Roe and Woodroofe (RW) have suggested that certain conditional probabilities be incorporated into the ``unified approach'' for constructing confidence intervals, previously described by Feldman and Cousins (FC). RW illustrated this…
An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…
An approach to testing theories describing a multiverse, that has gained interest of late, involves comparing theory-generated probability distributions over observables with their experimentally measured values. It is likely that such…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
In this paper, we continue to explore the consistence and usability of Probability Bracket Notation (PBN) proposed in our previous articles. After a brief review of PBN with dimensional analysis, we investigate probability spaces in terms…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
The purpose of quantization for a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonuniform probability measure $P$ on $\mathbb R^2$ which has support the Sierpi\'nski…
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the…